DOCSLIB.ORG

Quasiparticle Properties Under Interactions in Weyl and Nodal Line Semimetals

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quasiparticle Properties Under Interactions in Weyl and Nodal Line Semimetals www.nature.com/scientificreports OPEN Quasiparticle Properties under Interactions in Weyl and Nodal Line Semimetals Received: 23 July 2018 Jing Kang 1, Jianfei Zou1, Kai Li2, Shun-Li Yu3,4 & Lu-Bing Shao3,4 Accepted: 22 January 2019 The quasiparticle spectra of interacting Weyl and nodal-line semimetals on a cubic lattice are studied Published: xx xx xxxx using the cluster perturbation theory. By tracking the spectral functions under interaction, we fnd that the Weyl points will move to and meet at a specifc point in one Weyl semimetal model, while in the other Weyl semimetal model they are immobile. In the nodal-line semimetals, we fnd that the nodal line shrinks to a point and then disappears under interaction in one-nodal-line system. When we add another nodal line to this system, we fnd that the two nodal lines both shrink to specifc points, but the disappearing processes of the two nodal lines are not synchronized. We argue that the nontrivial evolution of Weyl points and nodal lines under interaction is due to the presence of symmetry breaking order, e.g., a ferromagnetic moment, in the framework of mean feld theory, whereas the stability of Weyl points under interaction is protected by symmetry. Among all these models, the spectral gap is fnally opened when the interaction is strong enough. Te discovery of semimetallic features in electronic band structures protected by the interplay of symmetry and topology provides a realistic platform for the concepts of fundamental physics theory in condensed matter phys- ics. In recent years, Weyl semimetals1–4 (WSM) have been attracted considerable attention since they extend the topological classifcation of mater beyond the insulators and exhibit the exotic Fermi arc surface state5. WSM 6,7 8,9 materials such as the TaAs-family pnictides and MoTe2 have been discovered by observation of the unique Fermi arcs of surface states through angle-resolved photoemission spectroscopy10–15. In these materials, the con- duction and valence bands touch each other around several points, which are called Weyl points (WPs), in the momentum space. Te WP acts as a topological monopole which can be quantifed by corresponding chiral charge through calculating the fux of Berry curvature16. According to the conservation of chirality, the WPs always exist in pairs of opposite chirality. Te topological Fermi arcs are arising from the connection of two projections of the bulk WPs with two opposite chiral charges in the surface Brillouin zone (BZ). WSMs and their surface states may lead to unusual spectroscopic and transport phenomena such as chiral anomaly, spin and anomalous Hall efects9. Te WSMs have a Fermi surface consisting of a fnite number of WPs in the BZ, at which the conduction and valence bands meet linearly. Te WPs are twofold degeneracy and only exist in condensed matter systems with breaking either time-reversal or spatial-inversion symmetry. Such a phase has massless Weyl quasiparticles which can be viewed as half-Dirac Fermions. Besides, the Weyl quasiparticles can be gapped by coupling two quasiparticles with diferent chirality17. In the presence of interactions which can easily arise in realistic systems, the Weyl quasiparticles can be moved, normalized and even gapped. Another interesting system is the nodal-line semimetal(NLSM) with one-dimensional Fermi surfaces18–21. In the experiment side, the NLSMs were observed 22 23,24 in several compounds such as PbTaSe2 and ZrSiS . In this system there are bulk band touchings along 1D lines and these line-like touchings need extra symmetries to be topologically protected. Interactions can also be applied in this system to discuss the proximity efect and spontaneous symmetry breaking25. In this paper, by using the Cluster Perturbation Teory (CPT)26–31, we study two lattice models for WSMs and one for NLSM to see how the on-site Coulomb interaction afects the WPs and nodal lines. In CPT, the quasipar- ticle spectral function can be calculated and then the positions of the WPs and nodal lines can be tracked through 1College of Science, Hohai University, Nanjing, 210098, China. 2School of Physics and Engineering, Zhengzhou University, Zhengzhou, 450001, China. 3National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, 210093, China. 4Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China. Correspondence and requests for materials should be addressed to J.K. (email: [email protected]) or K.L. (email: [email protected]) SCIENTIFIC REPORTS | (2019) 9:2824 | https://doi.org/10.1038/s41598-019-39258-3 1 www.nature.com/scientificreports/ www.nature.com/scientificreports Figure 1. (a) A 2 × 2 × 2-site cluster, as marked by numbers 1–8, in the cubic lattice. (b) Te scanning routine is Γ-X-M-Γ-R-X′-Γ in the bulk BZ. the spectral function when the interaction alters. We fnd that the WPs will move to and meet each other under interactions in one WSM model, while in the other WSM model they will not. In the one-nodal-line semimetal system, the nodal line shrinks to a point under interactions. When we add another nodal line to this system, we fnd that the two nodal lines will all shrink to specifc points one afer the other. We argue that the nontrivial evolution of WPs and nodal lines under interaction is due to the presence of symmetry breaking order, e.g., a ferromagnetic moment, in the framework of mean feld theory, whereas the stability of WPs under interaction is protected by symmetry. Among all these models, the spectral gap is fnally opened when the interaction is strong enough. Models and Methods Weyl Semimetal Models. We will consider two kinds of Weyl Semimetal Models. For the frst kind of WSM model (WSM1), the tight-binding Hamiltonian is written as follows16,32: =−† +− − σ Hc00∑k kx{[2(tkcoscoskm)(2coskkyzcos)] x ++2stkin yyσσ2stkin zz},ck (1) ††† where ckk= (,cc↑↓k ) and σx,y,z are the Pauli matrices. Te hopping constant t will be set t = 1 in calculations based on this model. Tis model breaks both time-reversal and space-inversion symmetries. Afer diagonalizing this non-interacting Hamiltonian, we can get the band structure =± −+−− 22++2 . εkx[2(coskkcos)0 mk(2 coscyzoskk)] 4sin yz4sin k (2) Assuming εk = 0, we get the WPs in the bulk BZ. Tere can be 2, 6 or 8 WPs for diferent parameter m, while two of the WPs are present at (±k0, 0, 0). We now introduce the second kind of WSM model (WSM2) which, in contrast to both the WSM1 and the second Weyl semimetal model studied in ref.16, preserves the space-inversion symmetry but not the time-reversal symmetry. Te tight-binding Hamiltonian is written as follows: =+† σσ+.σ Ht0 2[∑kckxcos(kkk)cxyos()yzcos( )]zkc (3) Similar to the second Weyl semimetal model studied in ref.16, the real space hopping is a type of bond-selective and spin-dependent Kitaev-like hopping31. Afer diagonalizing this non-interacting Hamiltonian, we can get the band structure =± 222++. εkx2ct os kkkcoscyzos (4) πππ Tis model gives us eight WPs at ±±,,± . ( 222) Nodal-Line Semimetal Model. For the NLSM model, the tight-binding Hamiltonian is written as follows25: † Hc01=+∑ kx{2[(tkcoscoskbyz−+)(tk23cos1−+)]σσxz2stkin yk},c k (5) SCIENTIFIC REPORTS | (2019) 9:2824 | https://doi.org/10.1038/s41598-019-39258-3 2 www.nature.com/scientificreports/ www.nature.com/scientificreports Figure 2. Intensity map of the spectral function A(k, ω) along high symmetry lines (see Fig. 1(b)) with m = 1.5 and k0 = 0.2π based on the WSM1 model for (a) U = 0, (b) U = 3, (c) U = 8 and (d) U = 9, respectively. Te red dashed lines denote the non-interacting band structures. where t1, t2, t3 are the hopping constants. We can also diagonalize the non-interacting Hamiltonian to get the band structure, which reads: =± +−+−2 +.22 εkx2[tk12(cos cos)kbyztk(cos 1)]stk3 in z (6) During our calculations based on this model, the hopping constant t1 will be set as the energy unit t1 = 1. By setting proper parameters t2, b, we can get one or two nodal lines. Interaction Hamiltonian. In order to investigate the efects of interactions in the semimetals, we use the Hubbard model =+ − μ HH0,Un∑∑i ii↑↓nn,,i i σ, (7) where H0 denotes a tight-binding Hamiltonian of the non-interacting semimetals as we have introduced above. U is the on-site Coulomb interaction, ni,σ is the particle-number operator on site i with spin σ and μ is the chemical potential which will be fxed μ = 1 U at half-flling as the band structures hold particle-hole symmetry. 2 Numerical Method. A good way to analyze the Hubbard model numerically is the exact diagonalization (ED). However, due to the limitation of computer memory capacity and speed of CPU, the solvable size of the lat- tice cannot be large. Tus one will not get enough momentum points to study the k-space distribution of the spec- tral function. Te CPT which is based on the ED is another numerical method to solve the Hubbard model26–28. Te Green’s function in a fnite size of lattice is frst calculated through the ED. Ten we can divide the whole lattice into many small lattices of this size which are usually called clusters. Te inter-cluster hopping is treated perturbatively and the Green’s function of the physical system is obtained from strong-coupling perturbation theory. As we get enough momentum points, we can track the evolution of WPs or nodal lines controlled by the variation of U. During our calculations, we choose a 2 × 2 × 2-site cluster in the cubic lattice shown in Fig.
Load more

Recommended publications
  • First-Principles Calculations and Model Hamiltonian Approaches to Electronic and Optical Properties of Defects, Interfaces and Nanostructures
    First-principles calculations and model Hamiltonian approaches to electronic and optical properties of defects, interfaces and nanostructures by Sangkook Choi A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Grauduate Division of the University of California, Berkeley Committee in charge: Professor Steven G. Louie, Chair Professor John Clarke Professor Mark Asta Fall 2013 First-principles calculations and model Hamiltonian approaches to electronic and optical properties of defects, interfaces and nanostructures Copyright 2013 by Sangkook Choi Abstract First principles calculations and model Hamiltonian approaches to electronic and optical properties of defects, interfaces and nanostructures By Sangkook Choi Doctor of Philosophy in Physics University of California, Berkeley Professor Steven G. Louie, Chair The dynamics of electrons governed by the Coulomb interaction determines a large portion of the observed phenomena of condensed matter. Thus, the understanding of electronic structure has played a key role in predicting the electronic and optical properties of materials. In this dissertation, I present some important applications of electronic structure theories for the theoretical calculation of these properties. In the first chapter, I review the basics necessary for two complementary electronic structure theories: model Hamiltonian approaches and first principles calculation. In the subsequent chapters, I further discuss the applications of these approaches to nanostructures (chapter II), interfaces (chapter III), and defects (chapter IV). The abstract of each section is as follows. ● Section II-1 The sensitive structural dependence of the optical properties of single-walled carbon nanotubes, which are dominated by excitons and tunable by changing diameter and chirality, makes them excellent candidates for optical devices.
    [Show full text]
  • 8.7 Hubbard Model
    OUP CORRECTED PROOF – FINAL, 12/6/2019, SPi 356 Models of Strongly Interacting Quantum Matter which is the lower edge of a continuum of excitations whose upper edge is bounded by ω(q) πJ cos (q/2). (8.544) = The continuum of excitations develops because spinons are always created in pairs, and therefore the momentum of the two spinons can be distributed in a continuum of different ways. Neutron scattering experiments on quasi-one-dimensional materials like KCuF3 have corroborated the picture outlined here (see, e.g. Tennant et al.,1995). In dimensions higher than one, separating a !ipped spin into a pair of kinks, or a magnon into a pair of spinons, costs energy, which thus con"nes spinons in dimensions d 2. ≥The next section we constructs the Hubbard model from "rst principles and then show how the Heisenberg model can be obtained from the Hubbard model for half- "lling and in the limit of strong on-site repulsion. 8.7 Hubbard model The Hubbard model presents one of the simplest ways to obtain an understanding of the mechanisms through which interactions between electrons in a solid can give rise to insulating versus conducting, magnetic, and even novel superconducting behaviour. The preceding sections of this chapter more or less neglected these interaction or correlation effects between the electrons in a solid, or treated them summarily in a mean-"eld or quasiparticle approach (cf. sections 8.2 to 8.5). While the Hubbard model was "rst discussed in quantum chemistry in the early 1950s (Pariser and Parr, 1953; Pople, 1953), it was introduced in its modern form and used to investigate condensed matter problems in the 1960s independently by Gutzwiller (1963), Hubbard (1963), and Kanamori (1963).
    [Show full text]
  • Effective Hamiltonians Derived from Equation-Of-Motion Coupled-Cluster
    Effective Hamiltonians derived from equation-of-motion coupled-cluster wave-functions: Theory and application to the Hubbard and Heisenberg Hamiltonians Pavel Pokhilkoa and Anna I. Krylova a Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 Effective Hamiltonians, which are commonly used for fitting experimental observ- ables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not triv- ial. In this contribution, we apply Bloch's formalism to equation-of-motion coupled- cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch's and des Cloizeaux's forms. We report the key equations and illustrate the theory by examples of systems with electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians are extracted directly from the so-obtained effective Hamiltonians. By making quantitative connections between many-body states and simple models, the approach also facilitates the analysis of the correlated wave functions. Artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed. I. INTRODUCTION Coarse graining is commonly used in computational chemistry and physics. It is ex- ploited in a number of classic models serving as a foundation of modern solid-state physics: tight binding[1, 2], Drude{Sommerfeld's model[3{5], Hubbard's [6] and Heisenberg's[7{9] Hamiltonians. These models explain macroscopic properties of materials through effective interactions whose strengths are treated as model parameters. The values of these pa- rameters are determined either from more sophisticated theoretical models or by fitting to experimental observables.
    [Show full text]
  • Holographic Topological Semimetals Arxiv:1911.07978V1 [Hep-Th]
    Holographic Topological Semimetals Karl Landsteiner Instituto de Física Teórica UAM/CSIC, C/ Nicolás Cabrera 13-15, Campus Cantoblanco, 28049, Spain E-mail: [email protected] Yan Liu Center for Gravitational Physics, Department of Space Science, Beihang University, Beijing 100191, China Key Laboratory of Space Environment Monitoring and Information Processing, Ministry of Industry and Information Technology, Beijing, China E-mail: [email protected] Ya-Wen Sun School of physics & CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China E-mail: [email protected] Abstract The holographic duality allows to construct and study models of strongly cou- pled quantum matter via dual gravitational theories. In general such models are characterized by the absence of quasiparticles, hydrodynamic behavior and Planck- ian dissipation times. One particular interesting class of quantum materials are ungapped topological semimetals which have many interesting properties from Hall transport to topologically protected edge states. We review the application of the holographic duality to this type of quantum matter including the construction of holographic Weyl semimetals, nodal line semimetals, quantum phase transition to arXiv:1911.07978v1 [hep-th] 18 Nov 2019 trivial states (ungapped and gapped), the holographic dual of Fermi arcs and how new unexpected transport properties,
    [Show full text]
  • Introduction to the Physical Properties of Graphene
    Introduction to the Physical Properties of Graphene Jean-No¨el FUCHS Mark Oliver GOERBIG Lecture Notes 2008 ii Contents 1 Introduction to Carbon Materials 1 1.1 TheCarbonAtomanditsHybridisations . 3 1.1.1 sp1 hybridisation ..................... 4 1.1.2 sp2 hybridisation – graphitic allotopes . 6 1.1.3 sp3 hybridisation – diamonds . 9 1.2 Crystal StructureofGrapheneand Graphite . 10 1.2.1 Graphene’s honeycomb lattice . 10 1.2.2 Graphene stacking – the different forms of graphite . 13 1.3 FabricationofGraphene . 16 1.3.1 Exfoliatedgraphene. 16 1.3.2 Epitaxialgraphene . 18 2 Electronic Band Structure of Graphene 21 2.1 Tight-Binding Model for Electrons on the Honeycomb Lattice 22 2.1.1 Bloch’stheorem. 23 2.1.2 Lattice with several atoms per unit cell . 24 2.1.3 Solution for graphene with nearest-neighbour and next- nearest-neighour hopping . 27 2.2 ContinuumLimit ......................... 33 2.3 Experimental Characterisation of the Electronic Band Structure 41 3 The Dirac Equation for Relativistic Fermions 45 3.1 RelativisticWaveEquations . 46 3.1.1 Relativistic Schr¨odinger/Klein-Gordon equation . ... 47 3.1.2 Diracequation ...................... 49 3.2 The2DDiracEquation. 53 3.2.1 Eigenstates of the 2D Dirac Hamiltonian . 54 3.2.2 Symmetries and Lorentz transformations . 55 iii iv 3.3 Physical Consequences of the Dirac Equation . 61 3.3.1 Minimal length for the localisation of a relativistic par- ticle ............................ 61 3.3.2 Velocity operator and “Zitterbewegung” . 61 3.3.3 Klein tunneling and the absence of backscattering . 61 Chapter 1 Introduction to Carbon Materials The experimental and theoretical study of graphene, two-dimensional (2D) graphite, is an extremely rapidly growing field of today’s condensed matter research.
    [Show full text]
  • Hear the Sound of Weyl Fermions
    PHYSICAL REVIEW X 9, 021053 (2019) Featured in Physics Hear the Sound of Weyl Fermions Zhida Song1,2 and Xi Dai1,* 1Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong 2Department of Physics, Princeton University, Princeton, New Jersey 08544, USA (Received 4 February 2019; revised manuscript received 10 April 2019; published 17 June 2019) Quasiparticles and collective modes are two fundamental aspects that characterize quantum matter in addition to its ground-state features. For example, the low-energy physics for Fermi-liquid phase in He-III is featured not only by fermionic quasiparticles near the chemical potential but also by fruitful collective modes in the long-wave limit, including several different sound waves that can propagate through it under different circumstances. On the other hand, it is very difficult for sound waves to be carried by electron liquid in ordinary metals due to the fact that long-range Coulomb interaction among electrons will generate a plasmon gap for ordinary electron density oscillation and thus prohibits the propagation of sound waves through it. In the present paper, we propose a unique type of acoustic collective mode in Weyl semimetals under magnetic field called chiral zero sound. Chiral zero sound can be stabilized under the so-called “chiral limit,” where the intravalley scattering time is much shorter than the intervalley one and propagates only along an external magnetic field for Weyl semimetals with multiple pairs of Weyl points. The sound velocity of chiral zero sound is proportional to the field strength in the weak field limit, whereas it oscillates dramatically in the strong field limit, generating an entirely new mechanism for quantum oscillations through the dynamics of neutral bosonic excitation, which may manifest itself in the thermal conductivity measurements under magnetic field.
    [Show full text]
  • Arxiv:2008.10628V3 [Cond-Mat.Str-El] 14 Jan 2021
    Prediction of Spin Polarized Fermi Arcs in Quasiparticle Interference of CeBi Zhao Huang,1 Christopher Lane,1, 2 Chao Cao,3 Guo-Xiang Zhi,4 Yu Liu,5 Christian E. Matt,5 Brinda Kuthanazhi,6, 7 Paul C. Canfield,6, 7 Dmitry Yarotski,2 A. J. Taylor,2 and Jian-Xin Zhu1, 2, * 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 2Center for Integrated Nanotechnology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 3Department of Physics, Hangzhou Normal University, Hangzhou 310036, China 4Department of Physics, Zhejiang University, Hangzhou 310013, China 5Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 6Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA 7Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA (Dated: January 15, 2021) We predict that CeBi in the ferromagnetic state is a Weyl semimetal. Our calculations within density func- tional theory show the existence of two pairs of Weyl nodes on the momentum path (0,0,kz) at 15 meV above and 100 meV below the Fermi level. Two corresponding Fermi arcs are obtained on surfaces of mirror- symmetric (010)-oriented slabs at E = 15 meV and both arcs are interrupted into three segments due to hy- bridization with a set of trivial surface bands. By studying the spin texture of surface states, we find the two Fermi arcs are strongly spin-polarized but in opposite directions, which can be detected by spin-polarized ARPES measurements. Our theoretical study of quasiparticle interference (QPI) for a nonmagnetic impurity at the Bi site also reveals several features related to the Fermi arcs.
    [Show full text]
  • The Limits of the Hubbard Model
    The Limits of the Hubbard Model David Grabovsky May 24, 2019 1 CONTENTS CONTENTS Contents 1 Introduction and Abstract 4 I The Hubbard Hamiltonian 5 2 Preliminaries 6 3 Derivation of the Hubbard Model 9 3.1 Obtaining the Hamiltonian . .9 3.2 Discussion: Energy Scales . 10 4 Variants and Conventions 12 5 Symmetries of the Hubbard Model 14 5.1 Discrete Symmetries . 14 5.2 Gauge Symmetries . 14 5.3 Particle-Hole Symmetry . 15 II Interaction Limits 17 6 The Fermi-Hubbard Model 18 6.1 Single Site: Strong Interactions . 18 6.2 Tight Binding: Weak Interactions . 20 7 The Bose-Hubbard Model 22 7.1 Single Site: Strong Interactions . 22 7.2 Tight Binding: Weak Interactions . 24 III Lattice Limits 25 8 Two Sites: Fermi-Hubbard 26 8.1 One Electron . 26 8.2 Two Electrons . 27 8.3 Three Electrons . 28 8.4 Complete Solution . 29 9 Two Sites: Bose-Hubbard 33 9.1 One and Two Bosons . 33 9.2 Many Bosons . 35 9.3 High-Temperature Limit . 36 10 Conclusions and Outlook 38 2 CONTENTS CONTENTS IV Appendices 40 A The Hubbard Model from Many-Body Theory 41 B Some Algebraic Results 42 C Fermi-Hubbard Limits 43 C.1 No Hopping . 43 C.2 No Interactions . 44 D Bose-Hubbard Limits 44 D.1 No Hopping . 44 D.2 No Interactions . 46 E Two-Site Thermodynamics 47 E.1 Fermi-Hubbard Model . 47 E.2 Bose-Hubbard Model . 49 F Tridiagonal Matrices and Recurrences 50 3 1 INTRODUCTION AND ABSTRACT 1 Introduction and Abstract The Hubbard model was originally written down in the 1960's as an attempt to describe the behavior of electrons in a solid [1].
    [Show full text]
  • Interaction and Temperature Effects on the Magneto-Optical Conductivity Of
    Interaction and temperature effects on the magneto-optical conductivity of Weyl liquids S. Acheche, R. Nourafkan, J. Padayasi, N. Martin, and A.-M. S. Tremblay D´epartement de physique; Institut quantique; and Regroupement qu´eb´ecois sur les mat´eriauxde pointe; Universit´ede Sherbrooke; Sherbrooke; Qu´ebec; Canada J1K 2R1 (Dated: July 29, 2020) Negative magnetoresistance is one of the manifestations of the chiral anomaly in Weyl semimetals. The magneto-optical conductivity also shows transitions between Landau levels that are not spaced as in an ordinary electron gas. How are such topological properties modified by interactions and temperature? We answer this question by studying a lattice model of Weyl semimetals with an on-site Hubbard interaction. Such an interacting Weyl semimetal, dubbed as Weyl liquid, may be realized in Mn3Sn. We solve that model with single-site dynamical mean-field theory. We find that in a Weyl liquid, quasiparticles can be characterized by a quasiparticle spectral weight Z, although their lifetime increases much more rapidly as frequency approaches zero than in an ordinary Fermi liquid. The negative magnetoresistance still exists, even though the slope of the linear dependence of the DC conductivity with respect to the magnetic field is decreased by the interaction. At elevated temperatures, a Weyl liquid crosses over to bad metallic behavior where the Drude peak becomes flat and featureless. We comment on the effect of a Zeeman term. I. INTRODUCTION nodes.11,12 This is a consequence of the parabolic density of states. It has been observed in the low-temperature, low-frequency optical spectroscopy of the known Weyl Weyl semimetals are three-dimensional (3D) analogs of 13 graphene with topologically protected band crossings and semimetal TaAs.
    [Show full text]
  • It's Been a Weyl Coming
    CONDENSED MATTER It’s been a Weyl coming Condensed-matter physics brings us quasiparticles that behave as massless fermions. B. Andrei Bernevig “Mathematizing may well be a creative activity of man, like language or music”1 — so said Hermann Weyl, the German physicist whose penchant for mathematical elegance prompted his prediction that a new particle would arise when the fermionic mass in the Dirac equation vanished2. Such a particle could carry charge but, unlike all known fermions, would be massless. During the course of his career, Weyl actually fell out of love with his prediction, largely because it implied the breaking of a particular symmetry, known as parity, which at the time was thought to be obeyed. More to the point, no such particle was observed during his lifetime. After his death, the Weyl fermion was proposed to describe neutrinos, which are now known to have mass. For some time, it seemed that the Weyl fermion was destined to be just an abstract concept from another beautiful mind. That was until the Weyl fermion entered the realm of condensed-matter physics. For several years this field has been considered fertile ground for finding the Weyl fermion. Now, three papers in Nature Physics3–5 have cemented earlier findings6,7 to confirm the predictions8,9 of Weyl physics in a family of nonmagnetic materials with broken inversion symmetry. In condensed-matter physics, specifically in solid-state band structures, Weyl fermions appear when two electronic bands cross. The crossing point is called a Weyl node, away from which the bands disperse linearly in the lattice momentum, giving rise to a special kind of semimetal.
    [Show full text]
  • Arxiv:2007.01582V2 [Quant-Ph] 15 Jul 2020
    Preparing symmetry broken ground states with variational quantum algorithms Nicolas Vogt,∗ Sebastian Zanker, Jan-Michael Reiner, and Michael Marthaler HQS Quantum Simulations GmbH Haid-und-Neu-Straße 7 76131 Karlsruhe, Germany Thomas Eckl and Anika Marusczyk Robert Bosch GmbH Robert-Bosch-Campus 1 71272 Renningen, Germany (Dated: July 16, 2020) One of the most promising applications for near term quantum computers is the simulation of physical quantum systems, particularly many-electron systems in chemistry and condensed matter physics. In solid state physics, finding the correct symmetry broken ground state of an interacting electron system is one of the central challenges. The Variational Hamiltonian Ansatz (VHA), a variational hybrid quantum-classical algorithm especially suited for finding the ground state of a solid state system, will in general not prepare a broken symmetry state unless the initial state is chosen to exhibit the correct symmetry. In this work, we discuss three variations of the VHA designed to find the correct broken symmetry states close to a transition point between different orders. As a test case we use the two-dimensional Hubbard model where we break the symmetry explicitly by means of external fields coupling to the Hamiltonian and calculate the response to these fields. For the calculation we simulate a gate-based quantum computer and also consider the effects of dephasing noise on the algorithms. We find that two of the three algorithms are in good agreement with the exact solution for the considered parameter range. The third algorithm agrees with the exact solution only for a part of the parameter regime, but is more robust with respect to dephasing compared to the other two algorithms.
    [Show full text]
  • Electronic Properties of Type-II Weyl Semimetal Wte2. a Review Perspective
    Electronic properties of type-II Weyl semimetal WTe2. A review perspective. P. K. Das1, D. Di Sante2, F. Cilento3, C. Bigi4, D. Kopic5, D. Soranzio5, A. Sterzi3, J. A. Krieger6,7,8, I. Vobornik9, J. Fujii9, T. Okuda10, V. N. Strocov6, M. B. H. Breese1,11, F. Parmigiani3,5, G. Rossi4,9, S. Picozzi12, R. Thomale2, G. Sangiovanni2, R. J. Cava13, and G. Panaccione9,* 1Singapore Synchrotron Light Source, National University of Singapore, 5 Research Link, 117603, Singapore 2Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland Campus Süd, Würzburg 97074, Germany 3Elettra - Sincrotrone Trieste S.C.p.A., Strada Statale 14, km 163.5, Trieste 34149, Italy 4Dipartimento di Fisica, Universitá di Milano, Via Celoria 16, I-20133 Milano, Italy 5Universitá degli Studi di Trieste - Via A. Valerio 2, Trieste 34127, Italy 6Paul Scherrer Institute, Swiss Light Source, CH-5232 Villigen, Switzerland 7Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland 8Laboratorium für Festkörperphysik, ETH Zürich, CH-8093 Zürich, Switzerland 9Istituto Officina dei Materiali (IOM)-CNR, Laboratorio TASC, in Area Science Park, S.S.14, Km 163.5, I- 34149 Trieste, Italy 10Hiroshima Synchrotron Radiation Center (HSRC), Hiroshima University, 2-313 Kagamiyama, Higashi- Hiroshima 739-0046, Japan. 11Department of Physics, National University of Singapore, 117576, Singapore 12Consiglio Nazionale delle Ricerche (CNR-SPIN), c/o Univ. Chieti-Pescara "G. D'Annunzio", 66100 Chieti, Italy 13Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA * Corresponding author: [email protected] Currently, there is a flurry of research interest on materials with an unconventional electronic structure, and we have already seen significant progress in their understanding and engineering towards real-life applications.
    [Show full text]